In a global change scenario, some climatic and extreme weather events are expected to increase in frequency and intensity and cause more social and economic impacts in several sectors, such as transportation systems and urban mobility. As presented in several papers in literature, the cost of repairing transport assets after either an urban flood or landslide represents a significant percentage of the total damage cost of several recent disasters around the world [1]; [2]; [3]; [4] and in Brazil [5]; [6]; [7].

To mitigate those impacts, evaluating the risk associated with disasters and the best ways to deal with them is necessary. Disaster risk reduction is aimed at preventing new and reducing existing disaster risks and managing residual risk, all of which contribute to strengthening resilience and achieving sustainable development [8].

For disaster risk reduction, vulnerability is a key concept. There are several types and meanings for vulnerability. According to [9], vulnerability represents “the characteristics of a person or group and their situation that influence their capacity to anticipate, cope with, resist and recover from the impact of a natural hazard (an extreme natural event or process)”. The UN Office for disaster risk reduction also includes assets and systems as subjects to vulnerability: “The conditions determined by physical, social, economic and environmental factors or processes which increase the susceptibility of an individual, a community, assets or systems to the impacts of hazards” [8].

The transportation systems’ literature also has different meanings for vulnerability [10]. For example, [11] suggested that network vulnerability should be understood as “susceptibility to incidents that can result in considerable reductions in road network serviceability”, and [12] understood network vulnerability as the extent of a failure to impact the original purpose of the system.

Vulnerability is a key idea in Network Science as well. Due to its generality in representing the system topology (relation among the elements on the system), Network Science approaches have been applied to a huge number of very different areas [13]. Section 2.3 presents a Systematic Literature Mapping of papers related to road networks, disasters, and network vulnerability. The listed works are predominantly from 2020, published in interdisciplinary and transport journals. The most frequent type of disasters and data origin are flooding/landsliding and USA/China.

This paper presents a formulation for a vulnerability index based on the efficiencies of the system of networks. It aims to locate the most vulnerable links in a transportation network and assess whether these links are susceptible to hazards and disruptions. The idea is presented as a case study on a set of highways mapped based on vulnerability index and disaster susceptibility data.

Using the (geo) graph approach, we represent the set of highways as a network. For the Santa Catarina State case study area, the road network presents 1,536 nodes/road segments and 2,101 directed edges/connections between road segments.

The topological vulnerability index is used to assess the potential impact of disruptions in a transportation network. In the context of the current analysis, this index’s distribution was highly inhomogeneous. It is demonstrated in Figure 3, where the distribution is shown on a double logarithmic scale. Using Clauset’s method [47], the power law fitting to the distribution resulted in an exponent of α = 2.475.

This finding suggests that the vulnerability of transportation networks is not evenly distributed, with some highways being significantly more vulnerable than others. Specifically, most highways have a low to moderate vulnerability (see Figure 4, segments in green and yellow), while a small subset is highly vulnerable (see Figure 4, segments in red). It indicates that efforts to enhance the resilience of transportation networks should be focused on the most vulnerable highways to ensure the most significant impact in reducing the risk of disruptions.

Another important question is about where the most vulnerable elements are, particularly whether they are close to the areas most susceptible to floods. Figure 4 shows the topological vulnerability index map for all highways in the study area. The four classes (colors in Figure 4) correspond to Low Vulnerability, Moderate Vulnerability, High Vulnerability, and Extremely High Vulnerability.

In the subset of the study area in Figure 4, it is possible to see some elements with a high topological vulnerability index close to urban areas susceptible to flood. In this area, in the cities of Rio Negrinho and Mafra, the BR-280 highway crosses the river. This area is marked by several records of floods in the rainy season (susceptibility component), which makes traffic in the region unfeasible (impact).

The highway BR-280 is one of the most important in Santa Catarina state, playing an important role in transporting goods to the ports of São Francisco do Sul and Itajaí (Figure 1). It also promotes the interconnection link between important regional cities, such as Joinville and Jaraguá do Sul. Thus, this highway has a large flow of people and goods.

Considering vulnerability (as a topological index) and susceptible areas, this representation is an important tool for stakeholders from the transportation sector concerning climate change, disaster risk reduction, and sustainable development agenda. Risk Knowledge, combining hazard and vulnerability, is the first pillar of an Early Warning System (EWS) [8]. Also, the transportation sector represents direct and indirect economic losses: the destruction of physical assets and the decline in economic value. In this work, the suggested representation adds knowledge about the potential losses to the disaster risk assessment.

In this paper, we represented the set of highways from our study area as a network and calculated the topological vulnerability index. Using the (geo) graphs approach [26]; [27], it was possible to represent the results in a Geographical Information System.

In our case study, in the south region of Brazil, there are some elements with a vulnerability index of approximately 5% - therefore, a flood impairing the traffic on this highway’s element can reduce the efficiency of this transportation network by approximately 5%. Also, elements with high topological vulnerability index are close to urban flood areas, for example, in Mafra and Rio Negrinho, where the BR-280 highway crosses the Negrinho River. This area is marked by several records of floods in the rainy season (susceptibility component), which makes traffic unfeasible in the region (impact). In the State of Santa Catarina, there is a heavy flow of people and goods, with important national and international ports and airports.

The topological vulnerability index associated with an element of a network (in our case, a highway segment) is a measure quantifying how the system reacts to damage on this element. Although it is a measure associated with the element, the topological vulnerability index contains information about the dynamics throughout the network [48]. The disaster triggering is local, but its impacts can be extended to a wider region. The topological vulnerability index captures this relation, and it is possibly the most important feature of this index.

According to the Sendai Framework for Disaster Risk Reduction 2015–2030, one of the most important documents in the Disaster Risk Reduction (DRR) guidelines, there is one global target related to “Substantially reduce disaster damage to critical infrastructure and disruption of basic services” [49]. Many critical infrastructures (such as roads) are of network type and can be modeled using the Network Science approach [13]. The topological vulnerability index is a network measure particularly interesting in the context of critical infrastructures. Developing a vulnerability map to disasters and their impacts on infrastructures is also aligned with the 2030 Agenda for Sustainable Development, particularly with the Sustainable Development Goals 9, 11, and 13, related to Infrastructures, Intelligent Cities, and Climate [50].

Mapping risk areas is an indispensable step to doing better urban planning and lessening the risk of disasters. This mapping can create a risk reduction plan, define priority areas for attention in the municipalities, make recommendations for works on infrastructure, and prepare municipal master plans. The mapping of risk areas for Santa Catarina follows the guidelines established by GIDES Project [51], which is a partnership between Brazil and Japan to strengthen the National Strategy for Integrated Management of Risks and Disasters. The project’s goal is to reduce the risks of disasters through non-structural preventive actions. The main results are improving assessment systems and risk mapping, warnings, and urban planning for disaster prevention.

A possible extension for this investigation is to draft risk scenarios considering other components, such as the dynamic exposure (daily traffic on each highway) and other kinds of vulnerability, for example, one based on traffic engineering parameters or the coverage of meteorological sensors [52].